Hopefully expect some small notes on how I attacked the problems by tomorrow afternoon (spoiler: a couple of small brute force scripts on small numbers for the two annoying problems [you know which two]).

Have a nice night, happy submitting.

]]>Answers are due by March 1, 2010 (as always double check the official site for changes!) and we hope to once again post solutions after that date. Please remember to refrain from discussing the problems until then.

Good luck to all.

]]>Bob replies, “No, that’s not fair! You’re probably going to win since you get more flips!”

“Fine!” answers Alice. “How about this? You flip the coin 2009 times and I’ll flip it 2010 times and if I get more Heads, I win. If you get more Heads, you win. And, if there’s a tie, we’ll say that you win too.” Bob shrugs his shoulders and agrees to play.

What’s the probability that Alice wins the game? Prove your answer. ]]>

A fair die is rolled repeatedly until two consecutive rolls are equal, at which point the game ends.

If we let S be the sum of the results of all of the rolls, is S more likely to be even or odd, or is it equally likely to be both?

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